Information on Result #705844
Linear OA(3226, 743, F3, 59) (dual of [743, 517, 60]-code), using construction XX applied to C1 = C([337,394]), C2 = C([336,391]), C3 = C1 + C2 = C([337,391]), and C∩ = C1 ∩ C2 = C([336,394]) based on
- linear OA(3220, 728, F3, 58) (dual of [728, 508, 59]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,394}, and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(3214, 728, F3, 56) (dual of [728, 514, 57]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,391}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(3223, 728, F3, 59) (dual of [728, 505, 60]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,394}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(3211, 728, F3, 55) (dual of [728, 517, 56]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,391}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3227, 744, F3, 59) (dual of [744, 517, 60]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3226, 371, F3, 2, 59) (dual of [(371, 2), 516, 60]-NRT-code) | [i] | OOA Folding | |